The dual (sup-inf) problem (see [1]}) reads:
for fixed \(u^\varepsilon _t\in V(\Omega _t)\) ,
find \(v^\varepsilon _t\in V(\Omega _t)\)  such that
\(\mathcal {L}^\varepsilon (u^\varepsilon _t, v^\varepsilon _t; \Omega _t)\le \mathcal {L}^\varepsilon (u, v^\varepsilon _t; \Omega _t)\quad \text{for all } u\in V(\Omega _t) .\) 
